In the framework of GP regression, one way to enhance the expressive power of the nonparametric model is, ironically, to form a linear combination of different kernels and treat the coefficients as hyper-parameters optimizing the evidence. The classic regression on Mauna Loa dataset in [1]} adopts the SE kernel along with rational quadratic and periodic kernels. One may also view the spectra mixture kernel [2]} as a special kernel composition. For Bayesian neural network, on the other hand, the prior function distribution induced by prior parameter distribution [3]}, [4]} encodes the expressive power. In practice, design of activation in a network was shown to yield good extrapolation [5]}. In the following two subsections, we shall introduce two ideas improving the expressivity associated with the trig network representation of GP.
